“Phase transition for level-set percolation of the membrane model”
Venerdì 15 Luglio 2022, ore 14:30 - Aula 2BC30 - Maximilian Nitzschner (NYU Courant Institute)
We consider level-set percolation for the Gaussian membrane model on the integer lattice in dimensions five and higher, and establish that as h varies, a non-trivial percolation phase transition for the level-set above level h occurs at some finite critical level, which is positive in high dimensions. Moreover, we demonstrate the existence of a strongly subcritical phase, in which we provide bounds for the connectivity function of the level-set above h, and a strongly supercritical phase, in which we characterize the geometry of the level-set above level h. As a pivotal tool, we present novel (conditional) decoupling inequalities for the membrane model, which are instrumental in the study of both the subcritical and supercritical phases of its level-sets.
This talk is based on joint work with Alberto Chiarini.